Related papers: Self-Organized Branching Processes: A Mean-Field T…
We develop a unified theory that encompasses the macroscopic dynamics of recurrent interactions of binary units within arbitrary network architectures. Using the martingale theory, our mathematical analysis provides a complete description…
The majority-vote (MV) model is one of the simplest nonequilibrium Ising-like model that exhibits a continuous order-disorder phase transition at a critical noise. In this paper, we present a quenched mean-field theory for the dynamics of…
We employ the eigen microstate approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely, the BTW model and the Manna model. In both models, phase transitions from the absorbing-state to the critical…
Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of…
Self-organized bistability (SOB) is the counterpart of 'self-organized criticality' (SOC), for systems tuning themselves to the edge of bistability of a discontinuous phase transition, rather than to the critical point of a continuous one.…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…
I review the concept of self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales. Several exact results are…
Epidemic spreading has been intensively studied in SIS epidemic model. Although the mean-field theory of SIS model has been widely used in the research, there is a lack of comparative results between different theoretical calculations, and…
Self-organized criticality is a well-established phenomenon, where a system dynamically tunes its structure to operate on the verge of a phase transition. Here, we show that the dynamics inside the self-organized critical state are…
Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…
The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common…
We study a 2D quasi-static discrete {\it crack} anti-plane model of a tectonic plate with long range elastic forces and quenched disorder. The plate is driven at its border and the load is transfered to all elements through elastic forces.…
We model the dynamics of avalanches in granular assemblies in partly filled rotating cylinders using a mean-field approach. We show that, upon varying the cylinder angular velocity $\omega$, the system undergoes a hysteresis cycle between…
A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion…
We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical…
Load balancing plays a crucial role in many large scale systems. Several different load balancing principles have been proposed in the literature, such as Join-Shortest-Queue (JSQ) and its variations, or Join-Below-Threshold. We provide a…
We revisit the problem of deriving the mean-field values of avalanche critical exponents in systems with absorbing states. These are well-known to coincide with those of an un-biased branching process. Here, we show that for at least 4…
This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…
We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical…
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a…